When $\mathrm{Min}{\left(G\right)}^{-1}$ has a clopen $\pi$-base

Lafuente-Rodriguez, Ramiro, and McGovern, Warren Wm.. "When ${\rm Min}(G)^{-1}$ has a clopen $\pi $-base." Mathematica Bohemica (2021): 69-89. <http://eudml.org/doc/297218>.

@article{Lafuente2021,
abstract = {It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and $T_1$, but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the $l$-group in question is weakly complemented. A slightly weaker topological property than having a base of clopen subsets is having a clopen $\pi $-base. Recall that a $\pi $-base is a collection of nonempty open subsets such that every nonempty open subset of the space contains a member of the $\pi $-base; obviously, a base is a $\pi $-base. In what follows we classify when the inverse topology on the space of prime subgroups has a clopen $\pi $-base.},
author = {Lafuente-Rodriguez, Ramiro, McGovern, Warren Wm.},
journal = {Mathematica Bohemica},
keywords = {lattice-ordered group; minimal prime subgroup; maximal $d$-subgroup; archimedean $l$-group; $\mathbf \{W\}$},
language = {eng},
number = {1},
pages = {69-89},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {When $\{\rm Min\}(G)^\{-1\}$ has a clopen $\pi $-base},
url = {http://eudml.org/doc/297218},
year = {2021},
}

TY - JOUR
AU - Lafuente-Rodriguez, Ramiro
AU - McGovern, Warren Wm.
TI - When ${\rm Min}(G)^{-1}$ has a clopen $\pi $-base
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 69
EP - 89
AB - It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and $T_1$, but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the $l$-group in question is weakly complemented. A slightly weaker topological property than having a base of clopen subsets is having a clopen $\pi $-base. Recall that a $\pi $-base is a collection of nonempty open subsets such that every nonempty open subset of the space contains a member of the $\pi $-base; obviously, a base is a $\pi $-base. In what follows we classify when the inverse topology on the space of prime subgroups has a clopen $\pi $-base.
LA - eng
KW - lattice-ordered group; minimal prime subgroup; maximal $d$-subgroup; archimedean $l$-group; $\mathbf {W}$
UR - http://eudml.org/doc/297218
ER -